{
  "abstract": "We study non-parametric bandits in which arms are evaluated using Cumulative Prospect Theory (CPT) rather than expected reward. We consider continuous action spaces with arm-dependent noise and propose Non-Parametric CPT Bandits ($\\mathtt{NPCB}$), an optimistic algorithm that decouples mean estimation from CPT-based decision-making. We prove CPT regret of order $\\widetilde{\\mathcal O}\\bigl(\\sqrt{T\\,\\dim_E(\\mathcal F,T^{-2})\\,\\log N(\\mathcal F,T^{-2},\\|\\cdot\\|_\\infty)}\\bigr)$, where $\\dim_E$ is the Eluder dimension of the function class $\\mathcal F$, $T$ is the time horizon, and $N$ is its covering number in the sup norm. This matches the order-wise regret of classical non-parametric bandits, showing that CPT risk sensitivity incurs no additional order-wise regret cost. We extend $\\mathtt{NPCB}$ to unknown noise CDFs, retaining the known-CDF mean-learning term and adding a CDF-learning cost governed by a distributional Eluder dimension. We also study Kernel-CPT bandits and obtain information-gain-based regret bounds for a broad range of kernels, matching the corresponding risk-neutral kernel rates up to logarithmic factors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06489",
  "author_total": 3,
  "authors": [
    {
      "name": "Devdan Dey"
    },
    {
      "name": "Sujoy Bhore"
    },
    {
      "name": "Avishek Ghosh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4w9phjbd66a76.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06489",
  "fulltext_url": null,
  "id": "4w9phjbd66a76",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06489",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06489",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4w9phjbd66a76.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:06Z",
      "native_id": "2611.06489",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06489"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Risk-Sensitive Non-Parametric and Kernel Bandits",
  "title_text": "Risk-Sensitive Non-Parametric and Kernel Bandits",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:32Z",
  "url": "https://research.draconitic.com/paper/4w9phjbd66a76",
  "venue": "arXiv",
  "versions": []
}